Understanding the Mechanics of Standing Waves

[zmike]

I don't understand how standing waves "can exist." A drawing of a standing wave in my textbook shows this (fixed end)

View attachment 118953

I was thinking that if the law of superposition was true then doesn't that mean that ALL the waves should cancel out and you would have a completely straight string (nodes)?

Can someone please explain how standing waves work?

thanks

 

[zmike]

Help please?

 

[Sojourner01]

I don't understand your problem. Each point on the brown wave is the sum of the amplitudes of the blue and green waves at that point in time. What's the difficulty?

 

[mbrmbrg]

I think that the diagram is trying to show two traveling waves (green and blue) combining to make one standing wave (red).
Focus on a max/min of the red wave and see what happens to the green and red waves. Then focus on a node of the red wave.
You'll see that ONLY at the nodes do the green and blue waves cancel each other. (Unless, of course, you throw up first. That is one dangerously dizzifying diagram you posted.)

 

[zmike]

The problem is I did a lab at school and I have to interperet the data from a string that created a standing wave. During the lab it appeared that there was two waves (one positive and one negative) at the SAME POSITION (on top of one another). I was thinking that since the law of superposition states that when waves collide the amplitude of the wave (when on top of one another) is the algebraic sum of the two waves. How is it possible that you have two waves , one positive and another negative in the same position with the same amp.

 

[mbrmbrg]

The problem is I did a lab at school and I have to interperet the data from a string that created a standing wave. During the lab it appeared that there was two waves (one positive and one negative) at the SAME POSITION (on top of one another). I was thinking that since the law of superposition states that when waves collide the amplitude of the wave (when on top of one another) is the algebraic sum of the two waves. How is it possible that you have two waves , one positive and another negative in the same position with the same amp.

Oh.We did a lab like that too, except it looked like a lot more than two waves when we did it. I assume that there is really only one wave at any given moment, but the wave moves so quickly that the human eye only sees the blur. (Like turning on a fan; even though there are, say, 3 distinct blades, you see a complete circle.)

 

[zmike]

I am still a bit uncertain on this concept, shouldn't there be no waves at all since all the waves should cancel out?

 

[mbrmbrg]

Putting the lab aside for a moment, do you see why the green and blue waves in the moving diagram don't cancel out?

 

[zmike]

no, why don't they cancel?

 

[mbrmbrg]

Oh, god. That diagram really does make me queasy.

Focus on a red maximum, and notice that when the red is maximum, the green and blue are also both maximum. Do same for red minimum. Then look at red node.

 

[zmike]

red maximum? I only see a black line in the center, and a blue and green wave. EDIT: Actually I just found out that the gif animation image setting was turned off.

 

[mbrmbrg]

You don't have a big reddish-brownish wave going on also??

 

[zmike]

no, I only had a green and blue wave. sry

 

[mbrmbrg]

That's pretty funny. Can you switch computers? Because the diagram you posted most definitely shows three waves.

 

[zmike]

I fixed it and it's working now

 

[mbrmbrg]

Wonderful. So do you understand why the red standing wave is a result of the green and blue waves?

 

[zmike]

yes but it doesn't look like the one in I saw in the lab? is that because the two waves on each side was because it was moving very fast?

 

[mbrmbrg]

I think so. Does post #6 make more sense now?

 

[zmike]

yes. thank you for all your help.